I agree, it is hard to find hard scientific evidence either way on whether it is good or not. I just switched because I wanted to see if it helped with tear stains (it did in our case, and could have been due to my citys water supply, ymmv), and because i really don't want to have my babies drinking water with any additives in it at all. Water should be water. We have used filtered water as well as natural spring water too.
All blood tests are normal here, no freaky mineral or electrolyte deficiencies since switching,
so I am happy with that and will continue using it.
Perhaps the reason switching to distilled helps so many is that their regular water supply just has too many minerals/chemicals in it? Pondering